Remark 3  A big source of convergence in distribution with respect to a
capacity is provided by convergence in capacity. Indeed, let \(\mu \)  be a
subadditive capacity. Since by Proposition 8.5, p. 98 in [1]}, if
\((f_{n})_{n}\)  is a sequence of random variables converging in capacity to \(f\) ,
then \((f_{n})_{n}\)  converges in distribution to \(f\)  with respect to the same
capacity, it easily follows that if a sequence \((F_{n})_{n}\)  of random
functions converges in capacity to the random function \(F\)  at \(t_{0}\in D\) , then it converges in distribution with respect to capacity, to the
random function \(F\)  at \(t_{0}\in D\) .

